It seems that the dock "only" recognises (mini) DisplayPort monitors.
The conversion to HDMI or DVI etc. must be done by the cable/adapter, i.e. it must be active.
If digitec has done everything correctly, these cables should work: https://www.digitec.ch/de...
Unfortunately I don't have a Surface or Dock to test this myself.

I have a different problem:

Setup:
- Surface Book 2
- Surface Dock
- HP E233 screen connected to Surface Dock with a Displayport cable.
- Connection from Surface Dock to Surface Book 2

When I watch a video in the Surface Book 2 and connect the device to the Surface Dock, the Surface immediately shuts down.
Then I can restart it (hold down the power button for a long time). Then the external screen also works.
I have the same problem when I undock the screen of the Surface Book 2 and undock it again.

Does anyone have a solution to my problem?

I have exactly the same problem. Newest Surface Book with Performance Base and the Surface Dock. First external monitor connected to dock via HDMI cable and original Surface adapter (Mini DP to HDMI) -> no signal, rsp. keeps losing signal. Connected directly to Surface Book, I can work on the monitor without problems (so not a cable/adapter problem, I think). Windows updates up to date, dock update done. I won't even start on the second external monitor, as it's probably not possible to use older ones :(
Maybe someone has solved the problem in the meantime?

Updating the Surface to the latest version solves the problem.

It probably has something to do with the age of the monitors. In tests with 5 monitors and various adapters (DVI, HDMI, DisplayPort), it only worked with 2 older monitors directly from the Surface and not from the dock. I only tested with passive adapters.